We propose a description for the quasiequilibrium self-assembly of small, single-stranded (ss) RNA viruses whose capsid proteins (CPs) have flexible, positively charged, disordered tails that associate with the negatively charged RNA genome molecules. We describe the assembly of such viruses as the interplay between two coupled phase-transition-like events: the formation of the protein shell (the capsid) by CPs and the condensation of a large ss viral RNA molecule. Electrostatic repulsion between the CPs competes with attractive hydrophobic interactions and attractive interaction between neutralized RNA segments mediated by the tail groups. An assembly diagram is derived in terms of the strength of attractive interactions between CPs and between CPs and the RNA molecules. It is compared with the results of recent studies of viral assembly. We demonstrate that the conventional theory of self-assembly, which does describe the assembly of empty capsids, is in general not applicable to the self-assembly of RNA-encapsidating virions.

In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.

We have developed a kinetic Monte Carlo numerical scheme, specifically suited to simulate structural transitions in crystalline materials, and implemented it for the case of epitaxial graphene on SiC. In this process, surface Si atoms selectively sublimate, while the residual C atoms rearrange from a position occupied in the SiC hexagonal lattice to the graphene honeycomb structure, modifying their hybridization (from $s{p}^3$ to $s{p}^2$) and bond partners (from Si-C to C-C). The model is based on the assumption that the Monte Carlo particles follow the evolution of their reference crystal until they experience a thermally activated reversible transition to another crystal structure. We demonstrate that, in a formulation based on three parallel lattices, the method is able to recover the complex evolution steps of epitaxial graphene on SiC. Moreover, the simulation results are in noteworthy agreement with the overall experimental scenario, both when varying the structural properties of the material (e.g., the initial surface configuration or polarity) as well as the process conditions (e.g., the temperature and pressure).

We study the formation of a vortex with fourfold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observe five other regimes in the system: a homogeneous gaseous phase, band structures, moving clumps, moving clusters, and vibrating rings. All six regimes emerge from controlling the strength of noise and from the contribution of repulsion and alignment interactions. We study the shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. We derive hydrodynamical equations with an introduction of the “small deviation” technique to describe the vortex phase. The method is applicable to other systems as well. Finally, we compare the theory with the results of both computer simulations and an experiment using Quincke rotors. A good agreement between the three is observed.

In this work, we investigate the phase transitions and critical behaviors of the frustrated $J_1-J_2-J_3$ Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second-next-nearest-neighbor interaction $J_3$ on the phase transition from a disordered state to the single stripe antiferromagnetic state. A continuous Ashkin-Teller–like transition behavior in a certain range of $J_3$ is identified, while the four-state Potts-critical end point ${\left[J_3/J_1\right]}_C$ is estimated based on the analytic method reported in earlier work [Jin, Sen, and Sandvik, Phys. Rev. Lett. 108, 045702 (2012)]. It is suggested that the interaction $J_3$ can tune the transition temperature and in turn modulate the critical behaviors of the frustrated model. Furthermore, it is revealed that an antiferromagnetic $J_3$ can stabilize the staggered dimer state via a phase transition of strong first-order character.

The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated as either static or time-varying, supposing the whole network is observed in the same time window. In this paper, we consider the epidemics spreading on a network which has both static and time-varying structures. Meanwhile, the time-varying part and the epidemic spreading are supposed to be of the same time scale. We introduce a static and activity-driven coupling (SADC) network model to characterize the coupling between the static (“strong”) structure and the dynamic (“weak”) structure. Epidemic thresholds of the SIS and SIR models are studied using the SADC model both analytically and numerically under various coupling strategies, where the strong structure is of homogeneous or heterogeneous degree distribution. Theoretical thresholds obtained from the SADC model can both recover and generalize the classical results in static and time-varying networks. It is demonstrated that a weak structure might make the epidemic threshold low in homogeneous networks but high in heterogeneous cases. Furthermore, we show that the weak structure has a substantive effect on the outbreak of the epidemics. This result might be useful in designing some efficient control strategies for epidemics spreading in networks.

Mammalian sperm cells are required to swim over long distances, typically around 1000-fold their own length. They must orient themselves and maintain a swimming motion to reach the ovum, or egg cell. Although the mechanism of long-distance navigation is still unclear, one possible mechanism, rheotaxis, was reported recently. This work investigates the mechanism of the rheotaxis in detail by simulating the motions of a sperm cell in shear flow adjacent to a flat surface. A phase diagram was developed to show the sperm's swimming motion under different shear rates, and for varying flagellum waveform conditions. The results showed that, under shear flow, the sperm is able to hydrodynamically change its swimming direction, allowing it to swim upwards against the flow, which suggests that the upward swimming of sperm cells can be explained using fluid mechanics, and this can then be used to further understand physiology of sperm cell navigation.

We determine the impact of resource renewal on the lifetime of a forager that depletes its environment and starves if it wanders too long without eating. In the framework of a minimal starving random-walk model with resource renewal, there are three universal classes of behavior as a function of the renewal time. For sufficiently rapid renewal, foragers are immortal, while foragers have a finite lifetime otherwise. In the specific case of one dimension, there is a third regime, for sufficiently slow renewal, in which the lifetime of the forager is independent of the renewal time. We outline an enumeration method to determine the mean lifetime of the forager in the mortal regime.

The friction and diffusion coefficients of rigid spherical colloidal particles dissolved in a fluid are determined from velocity and force autocorrelation functions by mesoscale hydrodynamic simulations. Colloids with both slip and no-slip boundary conditions are considered, which are embedded in fluids modeled by multiparticle collision dynamics with and without angular momentum conservation. For no-slip boundary conditions, hydrodynamics yields the well-known Stokes law, while for slip boundary conditions the lack of angular momentum conservation leads to a reduction of the hydrodynamic friction coefficient compared to the classical result. The colloid diffusion coefficient is determined by integration of the velocity autocorrelation function, where the numerical result at shorter times is combined with the theoretical hydrodynamic expression for longer times. The suitability of this approach is confirmed by simulations of sedimenting colloids. In general, we find only minor deviations from the Stokes-Einstein relation, which even disappear for larger colloids. Importantly, for colloids with slip boundary conditions, our simulation results contradict the frequently assumed additivity of local and hydrodynamic diffusion coefficients.

Segregation of polydisperse granular materials in rotating containers is a ubiquitous but still not satisfactorily understood phenomenon. This study describes axial segregation of bidisperse granular mixtures of glass beads in a spherical container, rotating about its horizontal axis. Depending on the filling fraction of the mixer and on the composition of the mixture, qualitatively different spontaneously formed patterns are observed. For technical applications, the well-localized segregated bands allow a convenient separation of individual components of the mixtures. It is particularly surprising that the initial compositions of the granular mixtures have a fundamental influence on the location of the segregated bands. This evidences a collective pattern forming mechanism. The spontaneous formation of these bands cannot simply be traced back to individual particle dynamics. Existing models for segregation in spherical mixers are critically examined and extensions are suggested.

The dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] is employed to model the growth of a single vapor bubble in a superheated liquid on a flat homogeneous substrate. The bubble spreading dynamics in the pool boiling regime has been numerically investigated for one-component van der Waals fluids close to the critical point, with a focus on the effect of the substrate wettability on bubble growth and contact line motion. The substrate wettability is found to control the apparent contact angle and the rate of bubble growth (the rate of total evaporation), through which the contact line speed is determined. An approximate expression is derived for the contact line speed, showing good agreement with the simulation results. This demonstrates that the contact line speed is primarily governed by (1) the circular shape of interface (for slow bubble growth), (2) the constant apparent contact angle, and (3) the constant bubble growth rate. It follows that the contact line speed has a sensitive dependence on the substrate wettability via the apparent contact angle which also determines the bubble growth rate. Compared to hydrophilic surfaces, hydrophobic surfaces give rise to a thinner shape of bubble and a higher rate of total evaporation, which combine to result in a much faster contact line speed. This can be linked to the earlier formation of a vapor film and hence the onset of boiling crisis.

Using the field theoretic renormalization group technique in the second-order (two-loop) approximation the explicit expression for the turbulent vector Prandtl number in the framework of the general $A$ model of passively advected vector field by the turbulent velocity field driven by the stochastic Navier-Stokes equation is found as the function of the spatial dimension $d>2$. The behavior of the turbulent vector Prandtl number as the function of the spatial dimension $d$ is investigated in detail especially for three physically important special cases, namely, for the passive advection of the magnetic field in a conductive turbulent environment in the framework of the kinematic MHD turbulence $\left(A=1\right)$, for the passive admixture of a vector impurity by the Navier-Stokes turbulent flow $\left(A=0\right)$, and for the model of linearized Navier-Stokes equation $\left(A=-1\right)$. It is shown that the turbulent vector Prandtl number in the framework of the $A=-1$ model is exactly determined already in the one-loop approximation, i.e., that all higher-loop corrections vanish. At the same time, it is shown that it does not depend on spatial dimension $d$ and is equal to 1. On the other hand, it is shown that the turbulent magnetic Prandtl number $\left(A=1\right)$ and the turbulent vector Prandtl number in the model of a vector impurity $\left(A=0\right)$, which are essentially different at the one-loop level of approximation, become very close to each other when the two-loop corrections are taken into account. It is shown that their relative difference is less than $5\%$ for all integer values of the spatial dimension $d\ge 3$. Obtained results demonstrate strong universality of diffusion processes of passively advected scalar and vector quantities in fully symmetric incompressible turbulent environments.

We consider the nonmodal instability and transient growth of small disturbances in a plane-channel suspension flow with a nonuniform concentration profile of fine noncolloidal particles accumulated in two localized layers, symmetric about the channel axis. A single-velocity model of an effective Newtonian fluid with a finite particle volume fraction is employed. It is established that fine particles distributed nonuniformly in the main flow significantly modify the growth rate of the first mode in a wide range of governing parameters. The most pronounced destabilizing effect is produced by the particles localized in the vicinity of the walls. A parametric study of the so-called optimal disturbances showed that they are streaks elongated in the flow direction, similar to the optimal disturbances in the flow devoid of particles. The transverse wave number of the optimal disturbances depends strongly on the location of the particle layers. Even when the particle mass concentration (averaged over the channel cross section) is small (of the order of a percent) and the particles are localized in the middle between the walls and the channel axis, the energy of the optimal disturbances is by several orders of magnitude larger than in dusty-gas and pure-fluid flows. When the particle layers are located in the vicinity of the walls or the channel axis, the nonmodal instability mechanism is less pronounced, as compared to the flow devoid of particles.

Plasma is an ionized gas in which the collective behavior dominates over the individual particle interactions. For this reason, plasma is often treated as collisionless or collision-free. However, the discrete nature of the particles can be important, and often, the description of plasmas is incomplete without properly taking the discrete particle effects into account. The weak turbulence theory is a perturbative nonlinear theory, whose essential formalism was developed in the late 1950s and 1960s and continued on through the early 1980s. However, the standard material found in the literature does not treat the discrete particle effects and the associated fluctuations emitted spontaneously by thermal particles completely. Plasma particles emit electromagnetic fluctuations in all frequencies and wave vectors, but in the standard literature, the fluctuations are approximately treated by considering only those frequency-wave number regimes corresponding to the eigenmodes (or normal modes) satisfying the dispersion relations, while ignoring contributions from noneigenmodes. The present paper shows that the noneigenmode fluctuations modify the particle kinetic equation so that the generalized equation includes the Balescu-Lénard-Landau collision integral and also modify the wave kinetic equation to include not only the collisional damping term but also a term that depicts the bremsstrahlung emission of plasma normal modes.

We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal $-5/3$ scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The $-5/3$ scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a $-5/3$ exponent.

Nonequilibrium work relations such as Jarzynski equality and Crooks fluctuation theorem relate the free energy differences between two equilibrium states and the work distribution of nonequilibrium processes. We use the third constraint formulation of Tsallis statistics and derive the $q$-statistics generalization of nonequilibrium work relations.

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

Established populations often exhibit oscillations in their sizes that, in the deterministic theory, correspond to a limit cycle in the space of population sizes. If a population is isolated, the intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a stochastic version of the Rosenzweig-MacArthur predator-prey model. To this end we develop a WKB (Wentzel, Kramers and Brillouin) approximation to the master equation, employing the characteristic population size as the large parameter. Similar WKB theories have been developed previously in the context of population extinction from an attracting multipopulation fixed point. We evaluate the extinction rates and find the most probable paths to extinction from the limit cycle by applying Floquet theory to the dynamics of an effective four-dimensional WKB Hamiltonian. We show that the entropic barriers to extinction change in a nonanalytic way as the system passes through the Hopf bifurcation. We also study the subleading pre-exponential factors of the WKB approximation.

In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the interacting self-avoiding trail, and the vertex-interacting self-avoiding walk. These models are characterized by different microscopic interactions, giving rise, in the two-dimensional case, to collapse transitions of an apparently different nature. We expect that our results, even though of a mean-field type, could provide some useful information to elucidate the role of such different $\theta$ points in the polymer phase diagram. These issues are at the core of a long-standing unresolved debate.